Algebraic & Geometric Topology

Euclidean Mahler measure and twisted links

Daniel S Silver, Alexander Stoimenow, and Susan G Williams

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Abstract

If the twist numbers of a collection of oriented alternating link diagrams are bounded, then the Alexander polynomials of the corresponding links have bounded euclidean Mahler measure (see Definition 1.2). The converse assertion does not hold. Similarly, if a collection of oriented link diagrams, not necessarily alternating, have bounded twist numbers, then both the Jones polynomials and a parametrization of the 2–variable Homflypt polynomials of the corresponding links have bounded Mahler measure.

Article information

Source
Algebr. Geom. Topol., Volume 6, Number 2 (2006), 581-602.

Dates
Received: 26 March 2005
Accepted: 15 March 2006
First available in Project Euclid: 20 December 2017

Permanent link to this document
https://projecteuclid.org/euclid.agt/1513796536

Digital Object Identifier
doi:10.2140/agt.2006.6.581

Mathematical Reviews number (MathSciNet)
MR2220690

Zentralblatt MATH identifier
1096.57013

Subjects
Primary: 57M25: Knots and links in $S^3$ {For higher dimensions, see 57Q45}
Secondary: 37B40: Topological entropy

Keywords
link twist number Alexander polynomial Jones polynomial Mahler measure

Citation

Silver, Daniel S; Stoimenow, Alexander; Williams, Susan G. Euclidean Mahler measure and twisted links. Algebr. Geom. Topol. 6 (2006), no. 2, 581--602. doi:10.2140/agt.2006.6.581. https://projecteuclid.org/euclid.agt/1513796536


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